Electrical wave filter



IMPEDANCE REACTANCE IMPEDANCE ATTENUATION A. -J. GROSSMAN ELECTRICAL WAVE FILTER i 42 4 I j I/ FREQUENCY I f; f} FREQUENCY r, f r FREQUENCY FIG. 9

f f, FREQUENCY IMPEDANCE REACTANCE IMPEDANCE 4- FIG. 4

I 42 2/ /f l FREQUENCY I I ll I, I I I! A a '7 c a,

FIG. 6* n 1 4 l FREQUENCY x l G i 1 I I II I FIG. 8

I I '\j FREQUENCY a '7 2 I I INVENTO/P A.J.GRO$$MA/V B) ATTORNEY Patented Dec. I 11, 1935 UNl'iE' S TAThS PATENT creme ELECTRICAL WAVE FILTER Application December 29, 1933, Serial No. 704,442

24 Claims.

This invention relates to wave transmission networks and more particularly to electrical wave filters.

An object of the invention is to reduce the number of inductors or the number of capacitors required to construct a wave filter having specified transmission characteristics.

Another object is to reduce the total number of impedance elements'required for such a net- Work.

A further object is to reduce the space requirements and the manufacturing cost of wave filters.

A feature of the invention is a wave filter o1 the ladder type in which each impedance branch comprises two reactances of one type and one reactance of the other type.

In designing an electrical wave filter which will give a satisfactory performance under a given set of operating conditions, it is often found that the component reactance elements of one type are more expensive to build or require more space than the reactance elements of the other type. For example, if capacitances having large magnitudes and close adjustment limits must be provided, the capacitors may cost more than the inductors. On the other hand,'if large values of inductance are required with small energy dissipation at high frequencies, the inductors may be more expensive than the capacitors. Or, where space considerations are paramount, it may be found that the overall. size of the network may be reduced by-resorting to a filter design having a minimum number. of inductances. Also, the effective electrostatic and electromagnetic shielding of the filter is considerably simplified by reducing the number of-inductors used. Then too, as a rule, both the size and cost of a filter are reduced by a reduction in the total number of reactance elements required for its construction.

These objects are achieved, in accordance with the present invention, by the provision of two new filter sections of the ladder type in which each series and each shunt impedance branch comprises two reactance elements of one type and one reactance element of the other type. Thus, a single full section of the unbalanced type will consist either of six inductors and three capacitors, or of six capacitors and three inductors. The same attenuation characteristic may be provided as that obtainable with previously known single sections of the ladder type which require five inductors'and five capacitors, thus efiecting a saving of one element and thereby reducing the size and-cost of the filter. The new sections have the further advantage that the number of capacitors may be reduced from five to three", or the number of inductors may be reduced in like proportion, as compared with the prior art filters referred to above. The selection the section to be used in any particular instance is generally dictated by a consideration of the relative'costs of the two types of reactance elements.

Thenature of theinvention will be more fully understood from the following detailed description and by reference to the accompanying drawing, of which Figs. land 2 show schematically the full series full shunt impedance branches of the two filter sections of the invention;

Figs. 3 and 4 represent the reactance-characteristics of the impedance branches comprising the networks of Figs. 1 and 2;

Figs. 5 and 6 give symbolically the mid-series characteristic impedance of the filter sections of Figs; 1 and 2; respectively;

Figs. 7 and 8 are symbolic representations of the mid-shunt characteristic impedance of the filters shown in Figs. 1 and 2, respectively; and

Fig. 9 is a typical attenuation characteristic which may be obtained from the networks of Figs. 1 and 2.

The filter sections of the invention are of the well known ladder type, comprising lumped impedances Z1 connected. in series with the line and alternately disposed lumped impedances Z2 in shunt with the line. Each impedance branch comprises one reactance element offone type and two reactance elements of the other type, the reactance characteristic of each branch exhibiting one resonance frequency and one frequency of anti-resonance. I

In the'filter section represented schematically by Fig. 1 each impedance branch comprises two inductances and one capacitance. Typical reactance characteristics of these branches are shown in Fig.3, in which the solid line curve represents thereactance of the full-series branch 21 and dotted line curve represents four times the reactance of the full shunt branch Z2. In each branch the anti-resonance occurs at a lower frequency than the resonance, and it will be noted that the resonance frequency of Z1 coincides with the anti-resonance of Z2, both occurring at the frequency fc. The filter is of the band-pass variety, having two attenuation peaks, one on each side of' thetransmiss-i'on band, as shown by the attenuation characteristic of Fig.

9. The two cut-off frequencies f1, f2 occur at the frequencies where the reactances Z1 and 4 Z2 are equal in magnitude but opposite in sign, and may be located graphically on the diagram of Fig. 3, as indicated. The lower attenuation peak occurs at the frequency fa where Z1 is antiresonant, and the upper peak occurs at the resonance frequency ft of Z2. The mid-series characteristic impedance of the filter is shown in Fig. 5 and the mid-shunt characteristic impedance in Fig. 6, the resistance being shown by the solid line curve and the reactance by the dotted line curve.

Assuming that non-dissipative elements are used, the impedance of the filter throughout the transmission band is a pure resistance, varying with frequency. In order to reduce reflection losses, it is customary to match the load impedance connected to the terminals of the filter with the characteristic impedance at the midband frequency fm, which is equal to The design of the filter section shown in Fig. 1 involves the'determination of the values of the four inductances L1, L2, L3, L4 and the two capacitances C1, C2. Since there are six independent constants to be determined it follows that any six properties of the filter, dependent upon the values of the reactance elements but independent ofeach other, may be chosen at will. Two of these may be taken as the cut-off frequencies f1, f2, thus defining the range of free transmission, two more as the frequencies of maximum attenuation fa, fb, the fifth as the characteristic impedance R of the filter at the mid-band frequency fm, and the sixth is determined by the fact that the resonance in the series branch and the anti-resonance in the shunt branch both occur at the same frequency, in.

The general equations for the propagation constant P,' the mid-series characteristic impedance K1 and the mid-shunt characteristic impedance K2 of any ladder type network, in terms of the full series branch impedance Z1 and the full shunt branch impedance Z2 are the following:

DIS"

When the filter is terminated mid-series,

and when the filter is terminated mid-shunt,

It will be found desirable to make R substantially equal to the impedance of the load which is to be connected to the filter terminals, in order to reduce reflection losses at the point of juncture.

The other filter section of the invention is shown schematically in Fig. 2, in which each impedance branch comprises two capacitances and one inductance. The branches will have the reactance characteristics shown in Fig. 4, in which the solid line curve represents the reactance of Z1 and therdotted line curve represents four times the reactance of Z2. In each branch the resonance occurs at a lower frequency than the anti-resonance,,and itrwill also be observed that the resonant frequency of Z1 coincides with the anti-resonance frequency of Z2, both occur ring at the frequency fc. The attenuation char- 4 acteristic, shown in Fig. 9, is the same as that for the filter of Fig. l, the criteria for cut-off frequencies and attenuation peaks also being the same for the two filters. mid-shunt characteristic impedances are shown, 41 respectively, in Figs. 6 and 8. The formulae required for the determination of the four capacitances C3, C4, C5, Csand the two inductances L5, L6 are the following:

In the above equations the symbols F, M1 and M2 have the values given, respectively, by Equations (10), (11) and (12). When the filter is terminated mid-series,

The mid-series and the Theformule given above for the=determination oi the reactance elements apply-to-full series and full shunt impedance branches. If the filter is terminated mid-series, each reactance of the '5 terminating series impedance branch should have only half theimpedance indicated, that is, each inductance should be made only half the magnitude and each capacitance should'be made twice the magnitude given by the formulae.

Likewise, if the filter is terminated mid-shunt,

each element of the terminating shunt branch should be made to have twice the indicated impedance, each inductance being of twice the value and each capacitance only half the value 15 given by the formulae.

In a filter having. the impedance branches shown in Fig. 1, the total inductance of a branch of .thetype of Zzis greater than that of a mesh of the type ofZr, and the capacitance is smaller. However, theshunt branch may be transformed into a mesh having. the configuration of the series branch, or if desired the series branch may be transformed into the configuration of the shunt branch. Also, in a filter in which the branch impedances are of the form shown in Fig. 2, the sum of the capacitances comprising a branch of the type of Z1 is greater than that of a mesh having the form of Z2, and the inductance is smaller. But either the series or the shunt branch of the filter may be transformed ,into the configuration of the other branch, if

it is found advantageous to do so in any particular design. The method of making these transformations is well known in the art, being shown, for example, on pages 270 and 271 of K. S. Johnsons Transmission Circuits for Telephonic Communication, published by D. Van Nostrand Company, Inc.

' It will be noted that the attenuation characteristic of the filter sections as shown in Fig. 9 is of the same type as that provided by the sixelement sections shown in Figs. 18 and 19 of U. S. Patent No. 1,644,004, to O. J. ZobeLissued October 4, 1927. However, only nine reactance elements are required for a single full section of the filter of the present invention, whether terminated mid-series or mid-shunt, whereas a single full section of the filter shown in Fig. 18 of the above mentioned patent requires ten elements when mid-shunt terminations are used, and the filter shown in Fig. 19 of the same patent also requires ten elements when mid-series terminations are employed. Under these circumcal actance element, as compared with the previously known filter sections, by using the filter sections of the present invention. As stated above, the attenuation characteristics may be 60 made identical in both cases. If a multi-section filter is to be built, six additional reactance elements are required for each unbalanced full section added. The filter is, therefore, known as the six-element type.

A further marked advantage of the filter sections here presented is that the designer has the choice of a section which employs a preponderance of inductances or a preponderance of capacitances, in the ratio of two to one, and therefore he may select the section which uses the greater number of the elements which, under the given operating conditions, are the cheaper to build.

What is claimed is:

1. A ladder type wave filter section in which stances, it is therefore possible to save one reeach impedance branch comprises a plurality of reactance elements, a majority of said reactance elementsin each of said branches being of the same type as the majority of said reactance elements in each of the remaining branches.

2. A ladder type wave filter section in which each impedance branch comprises a plurality of reactance elements, a majority of said reactance elements in each ofsaid branches being positive inductances.

3. A ladder type wave filter section in which each impedance branch comprises a plurality of reactance elements, a majority of said reactance elements in each of said branches being capacitances.

4. A six-element ladder type wave filter in which a majority of the component reactance elements are of. one type.

5. A six-element ladder type wave filter section comprising an impedance branch in series with the line andjan impedance branch in shunt with the line, a majority of the reactance elements comprising said section being of the same type.

6. A six-element ladder type Wave filter in which a majority of the component reactance elements are inductances.

7. A six-element ladder type wave filter in which a majority of the component reactance elements are capacitances.

8. A six-element ladder type wave filter section comprising an impedance branch in series with the line and an impedance branch in shunt with the line, a majority of the reactance elements in each of said branches being of the same type.

9. A ladder type wave filter section having an attenuation peak on each side of the trans- U mission band, a majority of the reactance elements in each impedance branch being of the same type.

13. A ladder type wave filter section having an attenuation peak on each side of the transmission band, a majority of the reactance elements in each impedance branch being inductances.

14. A ladder type wave filter section having an attenuation peak on each side of the transmission band, a majority of the reactance elements in each impedance branch being capacitances.

15. A ladder type wave filter comprising an impedance branch in series with the line and an impedance branch in shunt with the line, each of said branches having the same number of reactance elements and a majority of the reactance elements comprising said filter being of the same type.

16. A ladder type wave filter comprising an impedance branch in series with the line and an impedance branch in shunt with the line, each of said branches having the same number of reactance elements and a majority of the reactance elements in each of said branches being of the same type.

17. A ladder type wave filter in which each impedance branch comprises three reactance elements, a majority of said elements being of. the same type,

18. A ladder type wave filter in which each impedance branch comprises three reactance elements, two of said elements being of one type and one of said elements being of the other type.

19. A six-element ladder type wave filter section having a peak of attenuation on each side of the transmission band, a majority of the component reactance elements comprising said section being of one type.

20. A six-element ladder type wave filter section comprising an impedance branch in series with the line and an impedance branch in shunt with the line, said section having an attenuation peak on each side of the transmission band, and a majority of the reactance elements in each of 0 said branches being of the same type.

tion in which each impedance branch has the same type of reactance characteristic.

22. A six-element ladder type wave filter section in which each impedance branch has the same type of reactance characteristic, a resonance frequency in one of said branches occurring at an anti-resonance frequency in the other of said branches.

23. A ladder type wave filter section in which the reactance characteristic of each impedance branch has a finite resonance frequency other than zero and a finite anti-resonance frequency. said resonance frequency occurring at a lower frequency than said anti-resonance frequency.

24. A ladder type wave filter section in which the reactance characteristic of each impedance branch has a finite anti-resonance frequency other than zero and a finite resonance frequency, said anti-resonance frequency occurring at a lower frequency than said resonance frequency.

ALEXANDER J. GROSSMAN. 

